The parallel between rotations and Lorentz transformations is even more striking if we introduce the rapidity tanh1 (v c) (a) Express the Lorentz transformation matrix A (Eq 12 24) in terms of , and compare it to the rotation matrix (Eq 1 29) In some respects rapidity is a more natural way to describe motion than velocity (b) Express the Einstein velocity addition law in terms of rapidity

Question: The parallel between rotations and Lorentz transformations is even more striking if we introduce the rapidity: = tanh1 (v/c). (a) Express the Lorentz transformation

The parallel between rotations and Lorentz transformations is even more striking if we introduce the rapidity: θ = tanh–1 (v/c).

(a) Express the Lorentz transformation matrix A (Eq. 12.24) in terms of θ, and compare it to the rotation matrix (Eq. 1.29). In some respects rapidity is a more natural way to describe motion than velocity.

(b) Express the Einstein velocity addition law in terms of rapidity.

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